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Title:Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation PDF Logo
Authors:Fournié, Michel
Düring, Bertram
Jüngel, Ansgar
Issue Date:2004
Series/Report no.:Discussion paper series / Universität Konstanz, Center of Finance and Econometrics (CoFE) 04/02
Abstract:A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.
Subjects:High-order compact finite differences
numerical convergence
viscosity solution
financial derivatives
Persistent Identifier of the first edition:urn:nbn:de:bsz:352-opus-11696
Document Type:Working Paper
Appears in Collections:CoFE-Diskussionspapiere, Universität Konstanz

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